Draw horizontal conductive lines on a piece of paper and place the bottom side of the paper in a container of water

Place a probe in the water that is connected to the GND pin of an Arduino

Connect the horizontal lines to pins on the Arduino

As the water is absorbed into up into the paper, it will reach the lines and short them to GND

Based on which pins are shorted to GND, you can tell what the water level is, and use that to determine the amount of time has passed

Can display the time on computer via Serial or on an LCD/LED display

Experiment with running high current through different hand-drawn traces on paper or other materials (take safety precautions!)

Design a scantron-like system, where you can input data into a microcontroller using index cards and conductive markings

Trip wire that pulls a section of cardboard away from the drawn on circuit that opens the "trip" circuit which sounds an alarm.

Board game that senses player pawn placement using the drawn on circuit paths.

Tic Tac Toe game that lights up the three in a row for each piece. An X will connect with different drawn on connection spots than the O piece.

Foam sword fighting game where blade is painted with conductive paint and cardboard vest has conductive "targets" that will score points when hit.

Karate practice using conductive paint on gloves and/or boots that score points on conductive "targets" worn on vest or buttoned/pinned to Gi/uniform.

Operation Maze game - maze is drawn with conductive paint. Player uses a stylus with battery to trace through the maze without touching the walls otherwise it sounds an alarm! Then other player's turn. Mazes can be drawn with different widths and lengths to alter difficulty.

Informational map - paper map has conductive paint "hotspots" for landmarks, POI, etc. that when tapped with conductive stylus (or finger?) will display info about the POI or even play an audio file / audio tour about that place.

Touch barcode - similar to a QR code with conductive spots along a 2D plane. Used for cases where the part/product must physically touch the reader to ensure correctness.

Cardboard wack a mole - conductive hammer with battery used to smash conductive paint covered moles that light up then go out when hit with hammer.

Longest path game - cardboard tiles have conductive paint drawn lines on them. As player places tiles to connect the lines they add resistance to the total line. Longer lines score higher points.

Learn Chess Game - each game piece has two conductive paint spots on the sides that run down to the bottom and connects to the board surface. When player touches these spots and completes the circuit the board knows which piece it is and which space it is on. It then lights up all the possible spaces that piece can move to.

Water level meter - similar to water clock idea as the water level grounds each drawn on line it can show a full/empty gauge. Rain gauge?

Plumb bob - wood, string, weight, and conductive paint will cause a light and/or sound when the line is level and plumb.

Door/window alarm - two pieces of cardboard with conductive paint are placed in door jamb or window sill and sounds alarm when pulled apart.